First tip: never forget you can give a card to someone who has less cards
Since, the Natron Zombie buries from your discard pile, do everything you can to encounter monsters when you have minimal (ideally 0) in your discard pile.
The approach I've used is to start at the locations that have only 1 or 2 monsters in the deck list. You have 0 in your discard at the start of the scenario so the Zombie isn't as scary. Also, since the scenario power banishes the monster you replace with the Natron Zombie, even if you fail to defeat the Natron Zombie, the "original" monster is gone. That means that if you can't get the Electricity trait against a Natron Zombie, just focus on minimizing your discard pile. Either succeed at the combat check to defeat or play something to reduce the damage if you fail. Or better yet, evade the Natron Zombie. No AYA power and the "original" monster is gone. You can use the scenario power to do so, especially if you can reduce the combat damage from the scenario power.
Then, head to the Canny Jackal and (if you have 5+ characters) Caravanserai for characters that can't get the Electricity trait. They contain 0 monsters so you won't risk the Natron Zombie.
Heal often if you can. In most scenarios, I wait to have 5 in my discard pile to maximize Cure, but here I would Cure earlier to keep my discard pile as small as possible.
Also, don't be afraid to scout ahead. Triggers are scary, but knowing that a monster (aka Natron Zombie) is coming is better.
If you can handle the villain's AYA check (Constitution or Fortitude) then chasing her around is a great move, since she will clear out all the banes and just leave boons behind in the closed location.
And lastly, give cards to other characters. Both times I played, there was one or two characters who were great at this scenario. They gave cards to the characters that didn't fair as well.
Those ideas have worked pretty well for me.
Our 4 player group MUST acquire a boon every other turn without loosing any boons to succeed.
Just to be sure - you know your discard pile counts towards the 21 goal, right?
We played this with 6-party and it was absolute loot fest. Hawkmoon's post above is very much a complete *walkthrough* for this scenario, so if you're doing all the right stuff and still failing - maybe you should give some more details with the difficulties you experience. There are maybe 3-4 locations with 0 or 1 monster in their decks, so even if you bury a card to the monster/Natron summon - you still have a whole deck of boons to acquire. Your party only needs to get to +16 cards in total, so emptying two location decks will either do it, or will leave you with no more than a handful more boons to acquire.
То reiterate some of Hawkmoons' advice, that also worked on our table:
- focus-fire the whole party on single locations, starting with those containing the least amount of monsters, until you empty them; Mavaro will be great if you got his "assist other players' power
- keep your Evades to just shrug off the Zombie
- keep weapons and spells that have "Ignore monster's AYA power"
- If you have non-bury damage prevention - don't be afraid to low-ball and lose the roll against Natron; it won't save you from the AYA bury, but it will save you blessings you can then use to acquire new boons
- try to heal and empty a player's discard pile when you know NAtron is lurking ahead
If Hawkmoon and Longshot's advice doesn't cover you, can you be more specific about your group makeup, Bidimus?